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Because mod(x) is not "smooth at x = 0.
Suppose f(x) = mod(x). Then f'(x), if it existed, would be the limit, as dx tends to 0, of [f(x+dx) - f(x)]/dx
= limit, as dx tends to o , of [mod(x+dx) - mod(x)]/dx
When x = 0, this simplifies to mod(dx)/dx
If dx > 0 then f'(x) = -1
and
if dx < 0 then f'(x) = +1
Consequently f'(0) does not exist and hence the derivative of mod(x) does not exist at x = 0.
Graphically, it is because at x = 0 the graph is not smooth but has an angle.
Because mod(x) is not "smooth at x = 0.
Suppose f(x) = mod(x). Then f'(x), if it existed, would be the limit, as dx tends to 0, of [f(x+dx) - f(x)]/dx
= limit, as dx tends to o , of [mod(x+dx) - mod(x)]/dx
When x = 0, this simplifies to mod(dx)/dx
If dx > 0 then f'(x) = -1
and
if dx < 0 then f'(x) = +1
Consequently f'(0) does not exist and hence the derivative of mod(x) does not exist at x = 0.
Graphically, it is because at x = 0 the graph is not smooth but has an angle.
Because mod(x) is not "smooth at x = 0.
Suppose f(x) = mod(x). Then f'(x), if it existed, would be the limit, as dx tends to 0, of [f(x+dx) - f(x)]/dx
= limit, as dx tends to o , of [mod(x+dx) - mod(x)]/dx
When x = 0, this simplifies to mod(dx)/dx
If dx > 0 then f'(x) = -1
and
if dx < 0 then f'(x) = +1
Consequently f'(0) does not exist and hence the derivative of mod(x) does not exist at x = 0.
Graphically, it is because at x = 0 the graph is not smooth but has an angle.
Because mod(x) is not "smooth at x = 0.
Suppose f(x) = mod(x). Then f'(x), if it existed, would be the limit, as dx tends to 0, of [f(x+dx) - f(x)]/dx
= limit, as dx tends to o , of [mod(x+dx) - mod(x)]/dx
When x = 0, this simplifies to mod(dx)/dx
If dx > 0 then f'(x) = -1
and
if dx < 0 then f'(x) = +1
Consequently f'(0) does not exist and hence the derivative of mod(x) does not exist at x = 0.
Graphically, it is because at x = 0 the graph is not smooth but has an angle.
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JordanBecause mod(x) is not "smooth at x = 0.
Suppose f(x) = mod(x). Then f'(x), if it existed, would be the limit, as dx tends to 0, of [f(x+dx) - f(x)]/dx
= limit, as dx tends to o , of [mod(x+dx) - mod(x)]/dx
When x = 0, this simplifies to mod(dx)/dx
If dx > 0 then f'(x) = -1
and
if dx < 0 then f'(x) = +1
Consequently f'(0) does not exist and hence the derivative of mod(x) does not exist at x = 0.
Graphically, it is because at x = 0 the graph is not smooth but has an angle.
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